There exists a well-established technique for acquiring digital X-ray images using a scanning electron microscope (SEM) and one or more X-ray detectors. This technique involves directing an electron beam sequentially over a grid of points on a specimen surface. At each grid point, measurements are made at a specific X-ray energy with a so-called “wavelength dispersive spectrometer” (WDS), or an X-ray energy spectrum is acquired and data are extracted from this spectrum for selected chemical elements of interest using an energy dispersive spectrometer (EDS). In the simplest case, these data consist of, say, N integrals of counts recorded in energy bands (or “windows”) surrounding the characteristic energy for each element of concern. When the full energy spectrum is available, more sophisticated techniques have been used to extract the area of each characteristic peak above background and correct for peak overlap and hence obtain the characteristic line intensity for the element of interest. Each data value is used as the “pixel” intensity at that grid point for the element of concern so, after scanning over all the grid points covering the field of view, a set of N digital images corresponding to the N chemical elements of interest is obtained.
These images are commonly referred to as “X-ray maps”. These are commonly displayed using a computer monitor using a separate colour or hue for each element. For example, the “silicon” map could be displayed in blue, the “iron” map in red, the “potassium” map in green, and the “calcium” map in yellow. See for example P. J. Statham and M. Jones “Elemental Mapping Using Digital Storage and Colour Display”, Scanning Vol. 3, 3 (1980) pp 169-171.
Images have also been combined by processing to show where certain elements co-exist in regions of a specimen. That is, once the original X-ray map data have been acquired, the images are inspected and then recombined in suitable combinations to reveal the distribution of phases in the specimen (where each phase consists of elements occurring in specific abundances and exhibits a colour distinct from other phases). See for example Statham and Jones, 1980 where Si (Blue), K (Yellow) and Fe(Red) maps are combined so that where two elements coexist and are above a threshold, a combination colour is shown (such as Blue+Yellow=Green, etc.) and where all three elements are present, white is displayed.
Information presented in this way has to be obtained by skilled operators who can select the right colours and manipulate the N digital images in a suitable manner.
In addition to the above technique that uses WDS or EDS for detection using an SEM for excitation, images representing some aspect of material content can also be produced by a variety of other sensors and excitation sources, for example: X-ray fluorescence (XRF), Electron Energy Loss spectroscopy (EELS), Particle Induced X-ray Emission (PIXE), Auger Electron Spectroscopy (AES), gamma-ray spectroscopy, Secondary Ion Mass Spectroscopy (SIMS), X-Ray Photoelectron Spectroscopy (XPS), Raman Spectroscopy, Magnetic Resonance Imaging (MRI), IR reflectometry and IR spectroscopy.
The collection of N images is sometimes referred to as a “multi-spectral” set of images and there is often a requirement to generate a single composite image that will highlight the location of different materials within a field of view. In some cases, more than one modality will be available so that signals from more than one sensor type can be obtained for a particular pixel position on the object so that in general the “multi-spectral” set could contain images from different modalities.
In the current context, a “multi-spectral” set of images is not the same as a “hyper-spectral” data set where, at each pixel, a series of contiguous channels of data are obtained that defines a full spectrum at each pixel. However, the “multi-spectral” and “hyper-spectral” data are obviously related because each spectrum in a “hyper-spectral” data set can be processed to generate one or more values which can be used as intensities for a “multi-spectral” set of images. For example, a full x-ray energy spectrum consisting of, say, 1024 channels of digital data for a single pixel could be processed to obtain the 4 intensities corresponding to characteristic x-ray lines for Si K, Fe K, K K and Ca K so that the full hyper-spectral “spectrum image” is converted to a multi-spectral set consisting of Si, Fe, K and Ca element maps. Each image in a multi-spectral set usually identifies the spatial distribution of a particular property such as the concentration of a particular element, the mean atomic number of the material or a particular wavelength of cathodoluminescence radiation and so on, so that each image in a multi-spectral set already conveys some information to the observer.
It is well known that colour images can be obtained by mixing images corresponding to the three primary colours: red, green and blue (R, G, B) (see for example, John J. Friel and Charles E. Lyman, “X-ray Mapping in Electron-Beam Instruments”, Microsc. Microanal. 12, 2-25, 2006, FIG. 14). If the intensity value at a particular pixel in one image is Xr, in a second image is Xg and in the third image is Xb, then the tuple (Xr, Xg, Xb) can be used to define the colour at the corresponding pixel in a single full colour image. If the first image represents the concentration of one chemical element and the other images represent concentrations of other elements, then if the first image is shown in red alongside the resultant full colour image, in regions where the first image has the dominant pixel intensity, the resultant image will also be red in appearance. Thus even though there will be regions of mixed colour, there is some intuitive correspondence between the original images and the resultant full colour image, In general, if N is 3 or less, a single full colour image can be constructed simply by assigning one of the primary components, R, G or B to each original image.
If N>3, it is not possible to combine all the images in this fundamental way because there are only 3 independent channels for a typical RGB colour display. However one strategy for generating a single colour image that shows material content is to manipulate the data in the N images in order to obtain 3 suitable images that can be encoded in R, G and B and then mix these three images to expose mixture colours at each pixel that will delineate material content. This approach is sometimes called colour image fusion and the aim is to maximise the information content in the resultant full colour image. To this end, multivariate statistical techniques such a principal component analysis (PCA) are often employed to generate the images corresponding to the first 3 principal components. Each of the three principal component images is assigned to R, G and B to form the final full colour image. This approach has been described and assessed in detail (see for example, V. Tsagaris and V. Anastassopoulos, International Journal of Remote Sensing, Vol. 26, No. 15, 10 Aug. 2005, 3241-3254).
In the case where the original N images correspond to chemical element distribution maps (for example element maps in EDS/SEM or maps for particular mass numbers in SIMS), the original maps are easy to interpret. However, when multivariate statistical approaches are used to extract components, each derived component image is a mathematical abstraction that does not necessarily bear any direct relationship to any of the original N images.
An improved approach is described in Kotula et al, Microsc. Microanal. 9, 1-17, 2003, where a method using multivariate statistical analysis (MSA) is described to analyse a hyperspectral data set where the abstract principal components are converted into physically meaningful “pure” components and thus colour component images. Selected component images are coloured and mixed or “fused” to form a resultant image that bears a direct relationship to the component images. However, there is no attempt to provide a visual connection between the resultant image and the distribution of individual chemical elements that would normally be shown as a series of x-ray elemental maps. FIG. 1 summarises this prior art and shows that there is no direct connection between the construction of x-ray elemental maps and the visualisation of components derived by MSA. A hyper-spectral data set is used to construct x-ray maps. Separately, multivariate statistical analysis is applied to the hyper-spectral data to generate component images which are then “fused” to generate a resultant colour image showing regions of different composition. Although this method generates a resultant colour image using MSA, the colour is not connected to the colours chosen for the x-ray maps.
When N>3, a simple approach is to assign a distinctive individual colour to each original image then sum all the colour contributions from all the images at each pixel. For each image the signal intensity at each pixel is used to modulate the r, g, b components while maintaining the same colour hue. For the resultant mixture image, the r, g and b values from all the individually-coloured original images are summed to obtain a single r, g, b value for every pixel position. If necessary, the resultant mixture image can be scaled so that none of the r, g or b values exceeds the maximum allowed by the display technology used. This approach works well when there is very little overlap between the bright pixels in the original images because in regions where one original image dominates, the same colour will appear in the resultant image. However, if several of the original images are similar in appearance, in pixels where these images dominate over the others, the resultant pixel colour will not correspond to any one of the original images so the correspondence between original image and resultant image will be lost. Furthermore, as the number of original images, N, increases, the perceptible difference between the colours assigned to each original image decreases. Therefore, to get any success with this method, it is invariably necessary for an expert to select a suitable subset of original images for mixing and ignore the others.
There is therefore a need in materials analysis applications to provide an automated method of processing a number of different input image datasets to form a combined image dataset in such a way that regions of the input images which contribute significantly to corresponding region in the combined image have a recognisable colour similarity between the respective regions of the input and combined images.